# Deformation theory of abelian categories

@article{Lowen2004DeformationTO, title={Deformation theory of abelian categories}, author={Wenty T. Lowen and Michel van den Bergh}, journal={Transactions of the American Mathematical Society}, year={2004}, volume={358}, pages={5441-5483} }

In this paper we develop the basic infinitesimal deformation theory of abelian categories. This theory yields a natural generalization of the well-known deformation theory of algebras developed by Gerstenhaber. As part of our deformation theory we define a notion of flatness for abelian categories. We show that various basic properties are preserved under flat deformations, and we construct several equivalences between deformation problems.

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